Change log for Magma V2.15-12 (Released 29/7/2009)

Abelian Extensions of Numebr Fields

·A problem in the computation of maximal orders of Abelian extentions has been fixed. In some situations this bug would cause an internal error.

Algebraic Curves

·Some bugs have been fixed in the Parametrization routines for rational curves and some runtime error messages have been moved to the top level of the primary parametrization intrinsics.

Commutative Algebra

·A crash when forming sums of modules has been fixed. Reported by J. Baird.

·A crash in NormalForm involving null sets or sequences has been fixed. Reported by M. Grassl.

Coxeter groups

·Error messages of the form "Not a reflection group" have been changed to "Not a real reflection group" as appropriate.

·Reflection groups can now be defined over number fields of categories other than FldRat, FldCyc, and FldNum (for example FldQuad).

·BasicDegrees and BasicCodegrees work for complex reflection groups as well as real reflection groups.

Groups

·The subgroup constructor for automorphisms groups has been extended to allow a set of generators, not just sequence and list as before. Request from K. Andersen.

·The isomorphism returned by IsIsomorphic has been modified to ensure that it has codomain the second argument to the function, rather than a subgroup equal to the second argument group.

·A bug in CharacterTable has been fixed. Bug caused a crash with a runtime error from the LLL machinery. Reported by M. Grassl.

·A new operation on permutations has been installed: TensorProduct. This is equivalent to converting the two permutations to matrices, taking tensor product of matrices, and converting back to a permutation. Request from J. Kimberley.

·A bug with homomorphisms from the trivial pc-group has been fixed. Bug reported by K. Andersen.

·A rare crash when computing the automorphism group of a p-group has been fixed. Bug reported by K. Andersen.

·A crash when calling the function DistinctExtensions in the situation where the module is the natural module of a matrix group has been fixed. Reported by K. Andersen.

·A bug in computing Subgroups, where many subgroups of large groups were missed, has been fixed. Galois Groups

·A problem with linear factors in reducible polynomials has been fixed. Reported by A-S. Elsenhans.

·A problem with not properly increasing p-adic precision has been fixed. Reported by J. KlÃ¼ners.

Integers

·Parameters in ECPP have been slightly modified to prevent an "inconclusive" result in IsPrime and PrimalityCertificate for certain "smallish" primes. Reported by J. Kimberley who provided 11 explicit examples of primes between 15 and 22 decimal digits. ECPP now correctly certifies each of these examples to be prime.

Multisets

·Some inefficiences in &* and &+ for multisets have been fixed. Reported by J. Kimberley.

Number Fields

·A bug in the indexed access to coefficients of elements in relative extensions has been fixed. Reported by M. Grassl.

·A bug in IsIsomorphic for relative number fields has been fixed. Without this fix, internal errors could happen. Reported by R. Cosset.

Polynomial Rings

·A problem with input checking for Hilbert90 over a finite field has been fixed. Wrong input could cause an internal error.

·A crash in bivariate factorization for high degree polynomials has been fixed. Reported by G. McGuire.

Sparse Matrices

·An inefficiency when multiplying a dense vector by a sparse matrix has been removed.

Strings

·Coercion of 1 into the strings universe is now allowed, thus allowing reduction multiplication of the empty sequence of strings. Reported by J. Kimberley.